The work investigates morphing of a thin circular plate induced by non-uniform heating. Due to transient heat transfer, temperature gradients develop within the plate, causing spontaneous bending and non-uniform contraction of the material. This change in local length ratios is described by a prescribed non-Euclidean metric. If such a metric cannot be fully realized, internal stresses develop in the plate, which may lead to the loss of axisymmetry and the formation of wrinkles.
A model of a simple prototypical system is developed, linking the transient thermal problem, the geometry of the prescribed metric, elastic equilibrium, and stability analysis. Based on this model, the critical times, the number of resulting wrinkles, and their amplitudes are determined. Qualitative experimental results confirm that the formation of wrinkles is not a direct consequence of the geometric non-realizability of the prescribed metric, but rather of the compressive membrane stresses that develop as a result. The critical mode of instability corresponds to two circumferential wrinkles and is the energetically most favorable equilibrium branch. It was also found that, in the regime considered, the plate realizes only a small fraction of the prescribed curvature, while most of the metric mismatch is accommodated in the form of membrane stresses.
Although the geometry considered is simple, it represents a fundamental system for investigating morphing structures with an imposed metric. The work therefore contributes to the understanding of the relationship between geometry, stresses, and stability, and provides a basis for future investigations of the inverse design problem of morphing structures.
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